1. Field of the Invention
The invention relates to a method for the acquisition of a set of projection images for the reconstruction of a three-dimensional image data set of an object to be examined that is arranged in an examination zone, said acquisition being performed by means of an X-ray device that includes an X-ray source and an X-ray detector, the X-ray source being displaced along a trajectory around the examination zone, said trajectory being situated essentially on a spherical surface, in order to acquire the projection images. The invention also relates to an X-ray device that is suitable for carrying out such a method.
2. Description of Related Art
The so-called cone beam-computed tomography technique aims to reconstruct a three-dimensional image of an object to be examined from a set of cone beam projections of this object. An examination device that is provided with a punctiform X-ray source as well as with a flat X-ray detector is used for the measurement of the cone beam projections. The object is situated between the source and the detector. While the object remains stationary, the source and the detector are moved around the object; during this displacement cone beam projections are measured at short intervals in space or in time. The source and the detector are usually rigidly coupled to one another and the connecting line between the source and the center of the detector always passes through a defined point that is referred to as the isocenter. The trajectory of the source also determines the trajectory of the detector in such a case. Moreover, when small mechanical inaccuracies are ignored, the trajectory of the source is situated on the surface of a sphere whose center constitutes the isocenter. The trajectory of the source can be described by an image a: [sxe2x88x92,s+]xe2x86x92R3, where s is a real parameter and a(s) denotes the position vector of the trajectory relative to a Cartesian system of co-ordinates, the center of which is situated at the isocenter. The reconstructed image of the object represents the spatial distribution of the X-ray attenuation coefficient in the examination zone. The image is calculated from the measured set of cone beam projections by means of a computer and a reconstruction algorithm.
Numerous conditions must be satisfied so as to enable an exact reconstruction of the X-ray attenuation coefficient. One of these conditions is indicated and substantiated, for example, by P. Grangeat in xe2x80x9cMathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transformxe2x80x9d, in G. T. Herman, A. K. Louis and F. Natterer, Mathematical Methods in Tomography, Vol. 1497 of the Lecture Notes in Mathematics, Springer Verlag, 1991, pp. 66 to 97. This condition is known as the completeness condition which stipulates that each plane that intersects the examination zone should also intersect the trajectory of the X-ray source. A trajectory that satisfies the completeness condition in relation to an examination zone will be deemed to be complete in relation to this examination zone hereinafter.
In the case of an isocentric examination device the examination zone is preferably an isocentric sphere B(rmax) having the radius rmax. The completeness condition can also be formulated differently for a spherical examination zone. In order to derive such an alternative formulation, first the set of all planes that intersect an arbitrary but fixed point a(s) of the trajectory as well as the sphere B(rmax) is considered. Each of these planes is unambiguously characterized by its normal vector in relation to the center of the sphere B(rmax), that is, the isocenter. Simple geometrical considerations that can be understood on the basis of FIG. 1 demonstrate that such normal vectors form a spherical cap U(a(s),rmax) where the associated sphere has the center a(s)/2 and the radius |a(s)/2|. When the parameter s is varied, and hence also the point a(s), the spherical cap U(a(s),rmax) is also varied. When the parameter s traverses the interval [sxe2x88x92,s+], a corresponding number of spherical caps is obtained. From a construction point of view this number of spherical caps contains exactly those normal vectors that are associated with those planes that intersect the trajectory as well as the spherical examination zone B(rmax). Thus, in order to satisfy the completeness condition, this number of spherical caps must fill the sphere B(rmax) completely. This is because if a void were present, the planes that are associated with the normal vectors in this void would intersect the examination zone but not the trajectory.
For a given trajectory and a given sphere B(rmax), a dense sub-set of the set comprising all spherical caps can be calculated and graphically represented by means of a computer and a suitable computer program, after which it can be visually checked whether these spherical caps fill the sphere B(rmax) without voids or not. As opposed to the first formulation of the completeness condition, the second formulation thus enables a visual test as to whether or not a given trajectory is complete in relation to a given sphere B(rmax).
It is to be noted that a plane trajectory, that is, a trajectory that is situated completely within one plane, cannot be complete. This is because all planes that extend parallel to the plane of the trajectory and differ therefrom do not intersect the trajectory. Notably a circular trajectory or a segment thereof cannot be complete. However, there are trajectories that are composed of plane segments and are complete. These trajectories include, for example two circles that have the same diameter and the same center and whose axes enclose an angle that is large enough relative to one another.
When the trajectory of the X-ray source is not complete, it can nevertheless be attempted to reconstruct an image of the object to be examined. Generally speaking, however, shortcomings in the image quality will have to be accepted in such a case.
The examination device, however, must also be capable of realizing the trajectory of the X-ray source. In medical applications the object to be examined is a part of a patient who is accommodated on an examination table and it must be ensured that the X-ray source and the X-ray detector do not collide with the object to be examined or with the support for the object.
The Philips INTEGRIS V5000 is an examination device in conformity with the state of the art. This examination device has a C-arm, one end of which supports an X-ray source while an X-ray detector is mounted at its other end. The object to be examined is arranged between the X-ray source and the X-ray detector. The C-arm is supported by a circular rail, so that it can be rotated about its axis. This so-called C-arm axis extends perpendicularly to the plane that contains the C-arm. The support for the C-arm is connected, via a pivot joint, to a so-called L-arm which itself is connected, via a further pivot joint, to a suspension device that is mounted on the ceiling. This suspension device can be displaced rectilinearly and horizontally. The three axes mentioned always intersect one another in one point, that is, the isocenter. An electric motor provides the controllable rotation of the X-ray source and the X-ray detector about the C-arm axis. Rotations about the other two axes are assisted by servomotors, but cannot be controlled. The acquisition of a set of cone beam projections of the object to be examined takes place during a revolution of the C-arm about the C-arm axis. Because of the absence of control, rotations about the other two axes are not possible during the acquisition of cone beam projections in the INTEGRIS V5000. The rotation of the C-arm about its C-arm axis leads to a semi-circular trajectory of the X-ray source. As has already been stated, such a trajectory is not complete.
A complete trajectory could in principle be composed from a plurality of semi-circles. The C-arm would then be positioned anew between the sub-examinations. However, that would be a time-consuming operation. For applications concerning the imaging of blood vessels, necessitating the administration of X-ray contrast media, moreover, the quantity of contrast medium to be administered would have to be increased.
It is an object of the present invention to provide a suitable method for the acquisition of a complete set of cone beam projections of an object to be examined that is arranged in an examination zone. It is also an object of the present invention to provide an X-ray device that is suitable for carrying out such a method.
This object is achieved by means of a method as disclosed in claim 1 and by means of an X-ray device as disclosed in claim 11, respectively. In accordance with the invention it is proposed to configure the trajectory in such a manner that the X-ray source can continuously follow the trajectory in order to acquire the set of projection images and that not all points of the trajectory are situated in a common plane.
In accordance with the first completeness condition, each plane that intersects the object to be examined must contain a point of the trajectory. When the trajectory is situated completely within a plane that intersects the object to be imaged, this trajectory does not satisfy the completeness condition. This is because each plane that is oriented parallel to the plane of the trajectory and intersects the object to be examined does not contain a point of the trajectory. Therefore, each trajectory that satisfies the completeness condition must be a three-dimensional curve, which means that it may not be situated in one plane.
Granted, the known trajectory that consists of two orthogonal circles is not situated in one plane and it also satisfies the completeness condition. However, it is configured in such a manner that the X-ray source is first rotated 360xc2x0 about a first axis of rotation and subsequently through 360xc2x0 about a second axis of rotation that extends perpendicularly to the first axis of rotation. Therefore, after a rotation about the first axis of rotation the X-ray source must be stopped and subsequently rotated about the second axis of rotation. Consequently, the trajectory cannot be followed continuously. In accordance with the invention, however, the X-ray source can be moved along a three-dimensional trajectory without having to be stopped. Consequently, the trajectory in accordance with the invention enables the acquisition of a complete set of projection images for a 3D image data set, that is, in a reliable and fast manner and in one operation. This contributes to the reconstruction of 3D images being essentially free from artefacts and inaccuracies.
In conformity with a preferred version of the present invention the trajectory is configured in such a manner that each plane that intersects the examination zone comprises at least one point of the trajectory. The completeness condition for the examination zone is thus satisfied, enabling accurate imaging of an object to be examined that is situated in the examination zone.
According to a preferred version of the present invention the trajectory forms a closed curve. A closed curve is characterized by the fact that after a finite time interval the X-ray source will return to its starting position when it is moved along the trajectory. It is thus possible to move the X-ray source several times along the trajectory around the object to be examined during the acquisition of projection images. Such a possibility is advantageous for the imaging of periodically moving organs such as the beating heart.
Preferably, the trajectory in accordance with the invention is a curve that is twice differentiable. When the time t at which the X-ray source is in the position a(t) of the trajectory is chosen as the curve parameter, the speed of the X-ray source will be given by the first derivative of the curve in time at any instant. Because the curve is twice differentiable, the first derivative exists. Furthermore, the first derivative is continuous because the curve is twice differentiable. The position of the X-ray source along the trajectory thus changes continuously as a function of time. Therefore, such a curve can be continuously followed by an X-ray source. In the case of an abrupt (meaning a discontinuous) change of the position of the X-ray source, however, it would be necessary to stop the X-ray source in such a location of abrupt change in order to follow the trajectory. Preferably, a trajectory in accordance with the invention is even chosen to be a curve that is continuously twice differentiable, notably with large radii of curvature. The accelerations occurring during the realization of the trajectory are thus kept small.
In accordance with the invention cone beam projections are preferably acquired as projection images.
The X-ray device in accordance with the invention is configured in such a manner that the X-ray source can continuously follow the trajectory in order to acquire the set of projection images and that not all points of the trajectory are situated in a common plane.
Preferably, the X-ray device in accordance with the invention is a C-arm system that includes a C-arm, the X-ray source being mounted at one end of said arm whereas the X-ray detector is connected to its other end. A C-arm enables the object to be examined to be arranged between the source and the detector. When the X-ray source is displaced along the trajectory, the X-ray detector performs a corresponding movement. The movement of the X-ray source around the object to be examined can be realized simply by movement of the C-arm.
The X-ray device is preferably constructed in such a manner that the C-arm is rotatable about a C-arm axis while at the same time the C-arm mount is rotatable about a propeller axis. The propeller axis and the C-arm axis extend perpendicularly to one another and have a common point of intersection, that is, the so-called isocenter. The straight connecting line between the focal spot of the X-ray source and the center of the detector also passes through the isocenter. The described arrangement of axes of rotation enables the X-ray source to be rotated on a spherical surface around the isocenter during a rotation around one of the axes of rotation. The object to be examined is arranged in the vicinity of the isocenter in order to acquire a 3D image data set. The propeller axis and the C-arm are situated essentially in a common plane. Upon rotation of the C-arm about the propeller axis, the sections of the C-arm whereto the X-ray source and the X-ray detector are attached are rotated about a common axis like the blades of a propeller. The rotation around the propeller axis may then amount to more than 360xc2x0 or a multiple thereof.
In a preferred embodiment the propeller axis remains the same during a rotation of the C-arm about the C-arm axis.
A practical embodiment of an X-ray device in accordance with the invention is provided with a first mount for the X-ray source and the X-ray detector. Furthermore, this mount is rotatable about a first axis and connected to a second mount. The second mount is rotatable about a second axis and connected to a third mount. The third mount is connected, either rigidly or rotatably, to the building or is rotatably or slideably connected to a chain of one or more further mounts which are successively connected to one another by way of pivot joints and ultimately to the building. The first and the second axis intersect in one point. When the third mount is rotatably connected to the building or to a fourth mount, this third axis also intersects the point of intersection of the first two axes. The movements about the two first axes of rotation take place motorically and in a controlled manner. If present, the fourth and all further mounts serve to position the point of intersection of the first two axes in the vicinity of the object to be examined.
The above X-ray device is preferably configured in such a manner that the first axis mount is a C-arm whose ends support the X-ray source and the X-ray detector, respectively. The second mount supports said C-arm by means of a circularly bent rail, so that the C-arm can be rotated about the first axis which will be referred to hereinafter as the C-arm axis. The rotation about the second axis results in a propeller-like motion of the C-arm about the propeller axis. The C-arm axis and the propeller axis extend perpendicularly to one another and have a common point of intersection, being the so-called isocenter. The straight connecting line between the focal spot of the X-ray tube and the center of the detector also extends through the isocenter. The X-ray source is moved by rotating the C-arm and its C-arm axis and the mount of the C-arm about the propeller axis. Both rotations are required for a complete trajectory. The configuration of the axes of rotation ensures that the trajectory of the X-ray source is situated when ignoring small mechanical inaccuracies) on the surface of a sphere that is centered relative to the isocenter. The object to be examined is arranged in the vicinity of the isocenter.
The first mount can again be constructed so as to be arc-shaped but is connected to the second mount via a pivot joint. The third mount supports the second mount by way of a circularly bent rail, thus enabling a rotary movement. In comparison with the first embodiment the order of the propeller axis and the C-arm axis is reversed.
Further versions of the method in accordance with the invention and further embodiments of the device in accordance with the invention are disclosed in the dependent claims. It is to be noted that the X-ray device in accordance with the invention may be elaborated in the same way or in a similar way as the method in accordance with the invention as disclosed in the claims that relate directly or indirectly to claim 1.